
where \([k] = \lbrace 1, \ldots , k\rbrace \) , \(k\)  is a receptive field, \(\psi \)  is an MLP and \(\odot \)  is the element-wise product. \(p(u,v)\)  decouples the readout function from subgraph generation as suggested in Figure REF .
This approach moves computation from edgewise operations e.g. generating subgraphs, to nodewise operations (generating sketches) that encapsulate the most relevant subgraph information for LP. We have shown that (i) GNN propagation is either not needed (structure features) or can be preprocessed globally (given features) (ii) structure features can be generated from sketches instead of subgraphs (iii) an edge pooling readout function performs as well as a graph pooling readout. In combination these approaches circumvent the need to explicitly construct subgraphs.
The resulting model efficiently combines node features and the graph structure without explicitly constructing subgraphs and is as efficient as GCN [1]}.
